He was placed on the Sex Offenders Register and granted bail as sentencing was deferred for reports.
Sheriff Alistair Carmichael also ordered Glamis Castle to be assessed for its suitability for a tagging order.
Bowes-Lyon, who as a 15-year-old walked behind Prince William in the Queen Mother's funeral cortege, stood with his head bowed as the charge was read to him.
Fiscal depute Lynne Mannion told the court: "The accused is the Earl of Strathmore. He resides at his ancestral home of Glamis Castle. He divides his time between the castle and a property in London."
The multi-millionaire landowner who is known as Sam, described himself to police as a farmer.
Formerly Lord Glamis, he became the 19th Earl of Strathmore when his father, Michael Bowes-Lyon, died aged 58 in 2016.
His father, known as the head of the Bowes-Lyon family, was the grandson of the Queen Mother's brother, also Michael Bowes-Lyon.
The court heard that at the time of the assault, Glamis Castle had been chosen to host several people over a weekend for a feature for a luxury lifestyle magazine.
The group were to enjoy gin tasting, helicopter rides, shooting and a tour of the castle.
On the first night, the victim noticed that no one was talking to Bowes-Lyon during dinner and so engaged him in conversation. He then took her outside to show her one of his classic cars.
The following evening, she went to bed after a black-tie dinner and Bowes-Lyon carried on drinking before entering her room uninvited at 1.20 am.
Mannion said: "She was asleep and was woken by knocking at the door."
The court heard that Bowes-Lyon was calling: "It's Sam. It's important. Please let me in."
Mannion continued: "The second she opened the door he pushed his way in and pushed her onto the bed. He was very drunk and smelled of cigarettes.
"She had no signal. He refused to leave."
After more than 20 minutes, she managed to get him out of the room and sent a series of messages asking for help.
The woman fled the castle in the morning and flew home to report the matter. Both Police Scotland and the Metropolitan Police were involved in the investigation.
Bowes-Lyon emailed an apology to the woman and offered another apology for his behaviour in court, saying he was "greatly ashamed" of his actions.
The aristocrat, who is friends with members of the Made in Chelsea cast and was named one of Britain's 50 Most Eligible Bachelors by Tatler in 2019, later gave police a "no comment" interview.
John Scott QC, defending, said: "He is truly sorry for what he accepts was shameful conduct."
He said Bowes-Lyon had since been to counselling to try and understand his behaviour.
In June 2020, Durham Police contacted the Earl for violating Covid-related travel restrictions.
In 2010, he was banned from driving for nine months after getting clocked riding his motorbike at 100mph on a 60mph stretch of road.
